The present invention relates generally to a method and a system for determining altitude of a flying object, and more particularly, to a method of determining altitude of a flying object based on a gradient wind error model for the Blanchard algorithm.
The measurement of altitude of an aircraft can be obtained by various approaches. For example, by installing an accelerometers in an inertial navigation system in the aircraft, the altitude can be determined from a measured acceleration in the vertical direction by performing a double time integration of the measured vertical acceleration. Unbounded errors often occur to the altitude obtained from the accelerometer since the acceleration bias leads to exponential growth in the altitude.
The other commonly approach for the altitude measurement of an aircraft is the barometric altimeter. The barometric altimeter provides the altitude information as a function of barometric pressure based on a direct relationship between pressure and altitude. Barometric altitude, also known as pressure altitude, is determined as a function of pressure based on a standard day model for the atmosphere. As the atmospheric conditions encountered by an aircraft usually differs from the conditions defined by the standard day model, significant error may occur.
Decades ago Blanchard proposed an algorithm for computing the altitude of a flying object from atmosphere and temperature data as determined by sensors on board the flying object. Unlike the previous algorithm of pressure-altitude, which used an average temperature based on a standard model, Blanchard had more flexibility to adjust for variations in temperature caused by non-standard days. In further development, Blanchard modified his algorithm by incorporating additional term involving the motion of the atmosphere. The pressure altitude obtained by the original Blanchard algorithm is referred as Blanchard altitude, which can be referred to xe2x80x9cA New Algorithm for Computing Inertial Altitude and Vertical Velocityxe2x80x9d by R. L. Blanchard, in IEEE Transaction on Aerospace and Electronic Systems, Vol. AES-7, November. The modified Blanchard algorithm can be referred to xe2x80x9cAn Improvement to an Algorithm for Computing Reference Altitudexe2x80x9d, IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-8, No. 5, September 1972.
The development of radar system and GPS in recent years enables the user to compute the accuracy of Blanchard algorithm. FIGS. 1 and 2 show the errors of altitude for flight number 1 and flight number 2 flying over the continental United States measured by original and modified Blanchard algorithms. The errors were computed by subtracting GPS altitude from the output of the Blanchard algorithms. In FIGS. 1 and 2, the curves labeled by xe2x80x9caxe2x80x9d and xe2x80x9cbxe2x80x9d show errors for the original and modified algorithms of Blanchard, while the curve c shows the latitude as a function of time for these two flights. The original algorithm appears to have a noticeable build-up of error whenever the latitude of the flight changes. When the latitude increases, the altitude error becomes larger in a positive sense indicating that the altitude estimated by Blanchard algorithm is too high. On the other hand, this indicates that the pressure is lower than expected.
The decrease in pressure with latitude in the upper atmosphere is well known in meteorology as shown in upper air chart in FIG. 3. FIGS. 1 and 2 demonstrate the improvement of the modified algorithm; yet, the improvement varies significantly. For flight number 1, there was still a large remaining error, while flight number 2 had a residual error comparable to the accuracy of GPS itself.
Although GPS and radar system provides an accurate altitude for the flying object, there may be periods of time when the signal is unavailable. A system relying on an external signal is more vulnerable than a system contained within the flying vehicle. Therefore, there is a need to provide a method for determining the altitude of a flying object with improved accuracy according to the data measured from an onboard inertial navigation and data system.
The present invention provides a gradient wind error model, based on the model, a more accurate altitude of a flying object can be determined by correcting the Blanchard algorithm. The method of determining the altitude of a flying object comprises the following steps. A Blanchard altitude of a flying object is computed. A non-Blanchard reference altitude of the flying object is measured. The non-Blanchard reference altitude is compared to the Blanchard altitude to obtain a correction factor of the Blanchard altitude. The correction factor of the Blanchard altitude is then input to a Kalman filter for processing, so as to compute a radius of jet stream curvature. A gradient wind correction factor is then computed as a function of the radius of jet stream curvature, such that the Blanchard altitude can be corrected in response to the gradient wind correction factor.
In the above method, the non-Blanchard reference altitude is measured by a GPS system, a radar measurement system, or a double integration of the acceleration of the flying object measured from an accelerometer. A Kalman filter is used to process the non-Blanchard reference altitude and the trajectory of the flying object for deriving the radius of the jet stream curvature.
In the step of deriving the radius of the jet stream curvature, the linear relationship between the non-Blanchard reference altitude and the trajectory and the radius of the radius of jet stream curvature. The relationship can be expressed as:                     ∂        z                    ∂                  (                      δ            ⁢                          xe2x80x83                        ⁢            h                    )                      =                  1        ⁢                  xe2x80x83                ⁢        and        ⁢                  xe2x80x83                ⁢                              ∂            z                                ∂                          (                              δ                ⁢                                  xe2x80x83                                ⁢                u                            )                                          =              -                              ∫            0            T                    ⁢                                    f              ⁡                              (                t                )                                      ⁢                          xe2x80x83                        ⁢                          ⅆ              t                                            ,
where z is the measurement data of altitude, xcex4h is the error of the trajectory, and xcex4u is the error of the inverse of the radius of the jet stream curvature, T is the total flying time of the flying object, and f(t) is a function of the flying time t. The gradient wind correction factor is the product of the inverse of the radius of the jet stream curvature and an integration of the function f(t) over the flying time.
After the radius of the jet stream curvature is obtained, the gradient wind correction factor can be computed by a product of the inverse of the radius of jet stream curvature and an integration of f(t) over the flying time.
The present invention further provides an inertial navigation and data system for implementing the gradient wind error model. The system comprises a Blanchard altitude computing processor, a reference altitude measurement system, an inertial measurement device, a Kalman filter, and a correction processor. The Blanchard altitude computing processor is used to compute a Blanchard altitude of the flying object based on temperature and pressure encountered thereby. The trajectory of the flying object is measured by the trajectory measurement device. The altitude measurement system is used to measure a non-Blanchard reference altitude. The trajectory and the non-Blanchard reference altitude are then input to the Kalman filter to compute the radius of jet stream curvature. The Blanchard altitude, the radius of jet stream curvature, and the trajectory are then input to the correction processor to compute a gradient wind correction factor, which is then used to correct the Blanchard altitude.